linear equations help

Jul 2010
18
0
Could anyone help me work out these simultaneous equations, i am really struggling.

A)
3p+q=5
p+3q=-1

B)
7y-9x-13=0
5y-8x-14=0

C)
3.2a -0.7b -0.47 = 0
2.4a +0.35b -0.265 = 0

D)
3r-2t=-0.2
r+s=2.4
4s-t=7.3

E)
i1 + i2 + i3 = 0
50 i1 + 30 i2 = 16
-20 i2 + 5 i3 = -6
 
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Jul 2010
58
27
Brazil
daniel123,

These are simple system of equations. How did you started it? Show us what you've done. Maybe you should try a few methods of solution to find one that fits well to you - Gaussin elimination, substitution, Cramer's rule, for example.
 
Jul 2010
456
138
u can use substitution in those simple equation but as u move to bigger systems of equations it could get a little a bit of messy :D

A) u can multiply second equation with (-3) and add it to the first ... so u'll get q ... after that just put q in any of those starting equations and get p...
or u can say \(\displaystyle q=5-3p \) that's from first one and put that q in second and solve... or any another way...

that way u can do all of your systems of equations :D

or u can look at it as determinants and solve that way ... :D (don't know are u familiar with that but there's system with complex numbers so i think u are) :D
 
Jul 2010
18
0
This is the way i have done but still, when i verify the answer, i get the one correct but not the other and i carnt see where im going wrong.
for example, question A:

3p+q=5
P+3q=-1

re-arranged:
q=5-3p

substittuted for q:
p + 3(5-3p) = -1
= p + 15 - 9p = -1
= 8p + 15 = -1
= 8p = -16
p=-2

Substittuted for p:
q= 5 - 3(-2)
= 5 - -6
q = 11

VERIFY:
3(-2) + 11
= -6 + 11
= 5 CORRECT

-2 + 3(11)
= -2 + 33
= 31 WRONG
 
Jul 2010
456
138
\(\displaystyle p=2 , q=-1 \)

u have typo mistake :D \(\displaystyle -8p=-16 \) ... not like you wrote :D

so \(\displaystyle p=2 \) not \(\displaystyle p=-2\) and rest will be fine :D
 
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Jul 2010
18
0
ok so im probably going to have to go through these one at a time, as im getting in-sufficent numbers

B)
7y - 9x - 13 = 0
5y - 8x - 12 = 0


So... here we go

35y - 56x - 98) - (35y - 45x - 65)
= 35y - 56x - 98 - 35y + 45x + 65
= -11x - 35
-11x - 35 = 0
-11x = 35
x = -3.18

substittuting for x

7y - 9x (-3.18) - 13 = 0
= 7y + -9.54 - 13 = 0
= 7y + 22.54 = 0
7y = 22.54
y = 3.22

x= -3.18 y=3.22

VERIFIED:
7(3.22) - 9(3.18) - 13 = 0 WRONG

5(3.22) - 8(-3.18) - 14 = 0 WRONG
 
Jul 2010
456
138
wait... what did u do there... :D

first equation multiply with let's say 5 , and second one with (-7) ... then u'll get

\(\displaystyle 35y-45x=65\)

\(\displaystyle -35y+56x=-98\)

now add first to second (sum) and then u get x, ... u know the rest :D

P.S. in your first post free member's are not the same as here ?
 
Jul 2010
456
138
B)

\(\displaystyle y=-2 \;; x=-3\)

C)

\(\displaystyle a= 0.125 \;; b=-0.1 \)

D)

\(\displaystyle r = 0.4 \;; t = 0.7\; ; s= 2\)

E)

\(\displaystyle i_1=0.2 \;; i_2=0.2\;; i_3=-0.4\)
 
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